Luneberg lens

ABSTRACT

In a coaxial assembly of parallel, circular elements of substantially the same maximum radius, the thickness and effective dielectric constant of each element at each radius from zero to the maximum, and the spacing of the elements, are such that the assembly acts as a cylindrical Luneberg lens. Suitably, each element has the same dimensions and is of the same dielectric material, and the elements are regularly spaced. The varying thickness of each element enables the assembly of spaced elements to satisfy a desired relation between equivalent dielectric constant and radius. The lens is suitable for highpower applications.

United States Patent [1 1 Fuller et al.

[ LUNEBERG LENS [75] Inventors: Keith Lewis Fuller; Anthony John Lambell, both of Salfords, near Redhill, England [73] Assignee: U.S. Philips Corporation, New

York, NY.

[22] Filed: Aug. 23, 1972 [21] Appl. No.1 282,894

[ Dec. 25, 1973 2,761,141 8/1956 Strandberg et al 343/911 L Primary ExaminerEli Lieberman Att0rneyFrank R. Trifari [57] ABSTRACT In a coaxial assembly of parallel, circular elements of substantially the same maximum radius, the thickness and effective dielectric constant of each element at each radius from zero to the maximum, and the spacing of the elements, are such that the assembly acts as a cylindrical Luneberg lens. Suitably, each element has the same dimensions and is of the same dielectric material, and the elements are regularly spaced.

The varying thickness of each element enables the assembly of spaced elements to satisfy a desired relation between equivalent dielectric constant and radius. The lens is suitable for high-power applications.

5 Claims, 4 Drawing Figures [52] US. Cl 343/911 L [51] Int. Cl. H0lq 15/08 [58] Field of Search 343/753, 755, 911 R, 343/911 L [56] References Cited UNITED STATES PATENTS 2,866,971 12/1958 Kelleher 343/911 L 2,801,412 7/1957 Maybury et al... 343/911 R 3,307,196 2/1967 Horst 343/911 L 3,427,627 2/1969 Horst 343/911 L t ll i l PATENTEDDEDZSISYS 8781.900

n I -/D Fig.1

mam w MD I i Fig.2

Fig.3

I LUNEBERG LENS This invention relates to a Luneberg lens of cylindrical form for focussing microwave radiation.

The most general form of cylindrical Luneberg lens may be defined as an axially symmetric refracting structure, the dielectric constant of which varies with radius and which is able to form geometrical images of two coaxial cylinders on each other.

A practical design for such a lens may have one of the cylinders of infinite radius; thus a parallel beam of radiation incident on the lens may be focussed to a line diametrically opposite the plane of incidence. In a particular embodiment of this design, if the dielectric constant A, of the lens material varies with radius r according to the relation where r,, is the external radius of the lens, the other cylinder is of radius r i.e., the focal line lies on the surface of the lens. Other relations can be used, and may give lenses with foci inside or outside the lens.

A lens according to a relation such as 1) can be used to produce a fan beam which may be scanned over any desired angle simply by moving a line source of radiation parallel to the lens axis over the surface of the lens. Similarly, several beams may be produced with a single lens by using appropriately positioned sources.

A known method of making a practical Luneberg lens has been to approximate the required variation in dielectric constant with a series of shells of graded dielectric constants. Such a method can be expensive as it may require to different dielectric shells which have to be accurately machined to fit together to form the lens. A further disadvantage, which may arise in the use of a lens for transmitting high powers, is the difficulty of dissipating the heat produced by dielectric losses.

This invention proposes a simplified construction for a cylindrical Luneberg lens, employing several elements which may be of the same size and material; such a lens is also advantageous for high-power applications.

According to the invention, a cylindrical Luneberg lens comprises a coaxial assembly of parallel, circular elements of substantially the same maximum radius, wherein the thickness and effective dielectric constant of each element at each radius from zero to the maximum, and the spacing of the elements, are such that the lens is substantially of the form defined.

Suitably, each element has the same dimensions and is of the same dielectric material, and the elements are substantially regularly spaced. However, an element may comprise components of different radii and the components may be of the same or different dielectric materials: in each case, the elements may be regularly spaced.

Embodiments of the invention will now be more fully described with reference to the accompanying diagrammatic drawings, in which:

FIG. 1 illustrates an array of dielectric sheets;

FIG. 2 shows a lens embodying the invention;

FIGS. 3 and 4 show designs of elements suitable for a lens embodying the invention.

Illustrated in FIG. I is an array of parallel, plane, parallel-sided sheets of a material of dielectric constant e,

regularly separated in free space. The equivalent dielectric constant of the array, s is given by e I +(t/ when the electric field E of an incident wave perpendicular to the plane of the paper is parallel to the sheets, and

when field E is perpendicular to the sheets, where t is the thickness of each sheet, and D is the spacing of the sheets (i.e., there is an interval D t) of free space between neighbouring sheets). These equations are not valid when the spacing is so great as to be comparable with the wavelength A of the incident radiation; in general, the relation (4) should be satisfied.

By varying the thickness of each of the sheets with distance from an axis perpendicular to them, a desired variation in equivalent dielectric constant, such as specified in relation (1), may be obtained. Thus, a cylindrical Luneberg lens may be constructed from a coaxial assembly of parallel circular elements, which may each be of the same size and may be of the same material. FIG. 2 is a side view of a lens embodying the invention; it consists of a number of identical piano-convex elements of thickness t at radius r, maximum thickness I and maximum radius r,,, with regular spacing D. The ratio t/D is calculated for values of r from zero to r,, from equation (2) or (3) (as appropriate) to give the variation required by relation (1).

Provided that a substantially correct value of t/D is obtained at each radius r, the cross-section of each element may be any convenient shape, such as planoconvex, as shown in FIG. 2, or double convex. Each element may be an integral piece of a single dielectric, or may comprise two or more component parts of the same or different dielectric materials. An element in which a cruved surface is approximated by a series of plane surfaces may suitably employ several components, and FIGS. 3 and 4 illustrate embodiments of this type. In FIG. 3, a plane-convex element is approximated by 3 flat discs of progressively greaterdiarneter in contact one w ith another, while FIG. 4 shows separated components. The maximum thickness of each element must in all cases be such that the spacing D of the elements is not so large as to be comparable with a wavelength.

Where an element comprises contiguous components of materials of different dielectric constants, or separated components, the value of e to be used in relation 2) or (3) (as appropriate) in determining t/D at any particular value of r is the effective dielectric constant of the entire element at that radius.

A practical embodiment similar to that of FIG. 2 has been constructed with four polystyrene discs (6 2.54); the dimensions were r 30 cm D 1.80 cm r 1.26 cm.

When fed from an E-plane sectoral horn with E perpendicular to the elements of the lens, the combination was found to operate satisfactorily over the range 8 12 Gl-lz, giving a fan beam of beamwidth and side-lobe level appropriate to the lens aperture and field distribution. In this embodiment, incident radiation was focussed along a vertical line at the periphery of the discs,

but the invention may equally well be applied to a Luneberg lens whose focus lies some distance from the surface of the lens.

The separation of the elements of the lens, as against the contiguous structure of a conventional Luneberg lens, exposes a large surface area for cooling by forced air circulation, and the lens is thus suitable for highpower applications.

We claim:

1. A cylindrical Luneberg lens for focussing incident microwave radiation, comprising a coaxial assembly of at least two parallel circular elements of substantially the same maximum radius each element having a substantially uniform dielectric constant, each element having a thickness measured parallel to the assembly axis that varies inversely as a function of the radial distance from said axis, the spacing between element centers measured parallel to the assembly axis being less than the quotient of the wave length of the incident microwave radiation divided by the square root of the dielectric constant of the element material, the combination of the thickness variation and the spacing between elements of uniform dielectric constant thereby resulting in a lens assembly having an effective dielectric constant that varies inversely as a function of the radial distance from the lens axis.

2. A Luneberg lens as claimed in claim 1, wherein each element has the same dimensions and is of the same dielectric material, and wherein the elements are substantially regularly spaced.

3. A Luneberg lens as claimed in claim 1, wherein an element comprises components of different radii.

4. A Luneberg lens as claimed in claim 3, wherein an element comprises components of different dielectric material.

5. A Luneberg lens as claimed in claim 3 wherein the elements are substantially regularly spaced.

yg g gg" UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,781,900 Dated December 25, 1973 Inventor(s) KEITH LEWIS FULLER andAN'II-IONY JOHN LAMBELL It iscertified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

I- ON THE TITLE PAGE 1 Insert the following where appropriate:

-[30] Foreign Application Priority Data August 23, 19711 Great Britian ..39407/71 IN THE SPECIFICATION Col. 1, line '15," "A should be Signed and sealed tliis 16th day of April 19714..

Attestfi. H

EDWARD M.FLETC ER,JR. C. MARSHALL DANN Attesting Officer Commissioner of Patents 

1. A cylindrical Luneberg lens for focussing incident microwave radiation, comprising a coaxial assembly of at least two parallel circular elements of substantially the same maximum radius each element having a substantially uniform dielectric constant, each element having a thickness measured parallel to the assembly axis that varies inversely as a function of the radial distance from said axis, the spacing between element centers measured parallel to the assembly axis being less than the quotient of the wave length of the incident microwave radiation divided by the square root of the dielectric constant of the element material, the combination of the thickness variation and the spacing between elements of uniform dielectric constant thereby resulting in a lens assembly having an effective dielectric constant that varies inversely as a function of the radial distance from the lens axis.
 2. A Luneberg lens as claimed in claim 1, wherein each element has the same dimensions and is of the same dielectric material, and wherein the elements are substantially regularly spaced.
 3. A Luneberg lens as claimed in claim 1, wherein an element comprises components of different radii.
 4. A Luneberg lens as claimed in claim 3, wherein an element comprises components of different dielectric material.
 5. A Luneberg lens as claimed in claim 3 wherein the elements are substantially regularly spaced. 